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Despite their successes, deep learning models struggle with tasks requiring complex reasoning and function composition. We present a theoretical and empirical investigation into the limitations of Structured State Space Models (SSMs) and…
Number sense is a core cognitive ability supporting various adaptive behaviors and is foundational for mathematical learning. Here, we study its emergence in unsupervised generative models through the lens of rate-distortion theory (RDT), a…
Computational chemistry has become an indispensable tool for generating data and insights, pervading all branches of experimental chemistry. Its most central concept is the potential energy hypersurface, key to all chemistry and materials…
Despite recent advances in the reasoning capabilities of Large Language Models (LLMs), improving the reasoning ability of Small Language Models (SLMs, e.g., up to 1.5B parameters) remains challenging. A key obstacle lies in the complexity…
Dynamic programming (DP) is an algorithmic design paradigm for the efficient, exact solution of otherwise intractable, combinatorial problems. However, DP algorithm design is often presented in an ad-hoc manner. It is sometimes difficult to…
Quantum embedding methods enable the study of large, strongly correlated quantum systems by (usually self-consistent) decomposition into computationally manageable subproblems, in the spirit of divide-and-conquer methods. Among these,…
Density matrix perturbation theory (DMPT) is known as a promising alternative to the Rayleigh-Schr\"odinger perturbation theory, in which the sum-over-state (SOS) is replaced by algorithms with perturbed density matrices as the input…
Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to…
Pre-trained large language models (LMs) struggle to perform logical reasoning reliably despite advances in scale and compositionality. In this work, we tackle this challenge through the lens of symbolic programming. We propose DSR-LM, a…
In this chapter, we present and discuss a new generalized proportional conflict redistribution rule. The Dezert-Smarandache extension of the Demster-Shafer theory has relaunched the studies on the combination rules especially for the…
A critical question about Large Language Models (LLMs) is whether their apparent deficiency in mathematical reasoning is inherent, or merely a result of insufficient exposure to high-quality mathematical data. To explore this, we developed…
The Dempster-Shafer theory of evidence has been widely applied in the field of information fusion under uncertainty. Most existing research focuses on combining evidence within the same frame of discernment. However, in real-world…
Decision Transformer (DT) is an innovative algorithm leveraging recent advances of the transformer architecture in reinforcement learning (RL). However, a notable limitation of DT is its reliance on recalling trajectories from datasets,…
Effective computational search holds great potential for aiding the discovery of High-Temperature Superconductors (HTSs), especially given the lack of systematic methods for their discovery. Recent progress has been made in this area with…
In the field of data mining and machine learning, commonly used classification models cannot effectively learn in unbalanced data. In order to balance the data distribution before model training, oversampling methods are often used to…
Decision Transformers (DT) play a crucial role in modern reinforcement learning, leveraging offline datasets to achieve impressive results across various domains. However, DT requires high-quality, comprehensive data to perform optimally.…
Calculating perturbation response properties of materials from first principles provides a vital link between theory and experiment, but is bottlenecked by the high computational cost. Here a general framework is proposed to perform density…
Large Language Models (LLMs) have demonstrated amazing capabilities in language generation, text comprehension, and knowledge reasoning. While a single powerful model can already handle multiple tasks, relying on a single perspective can…
Large language models (LLMs) are increasingly used in situations where human values are at stake, such as decision-making tasks that involve reasoning when performed by humans. We investigate the so-called reasoning capabilities of LLMs…
Mathematical reasoning remains challenging for LLMs due to complex logic and the need for precise computation. Existing methods enhance LLM reasoning by synthesizing datasets through problem rephrasing, but face issues with generation…